Integral conditions for Hardy-type operators involving suprema

• Autores: Martin Krepela
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 68, Fasc. 1, 2017, págs. 21-50
• Idioma: inglés
• DOI: 10.1007/s13348-016-0170-6
• Texto completo no disponible (Saber más ...)
• Resumen

  • We characterize the validity of the weighted inequality \begin{aligned} \left( \int _0^\infty \Big [ \sup _{s\in [t,\infty )} u(s) \int _s^\infty g(x)\,\mathrm {d}x\Big ]^q w(t)\,\mathrm {d}t\right) ^\frac{1}{q} \le C \left( \int _0^\infty g^p(t) v(t)\,\mathrm {d}t\right) ^\frac{1}{p} \end{aligned} for all nonnegative functions g on (0,\infty ), with exponents in the range 1\le p<\infty and 0

    Moreover, we give an integral characterization of the inequality \begin{aligned} \left( \int _0^\infty \Big [ \sup _{s\in [t,\infty )} u(s) f(s) \Big ]^q w(t)\,\mathrm {d}t\right) ^\frac{1}{q} \le C \left( \int _0^\infty f^p(t) v(t)\,\mathrm {d}t\right) ^\frac{1}{p} \end{aligned} being satisfied for all nonnegative nonincreasing functions f on (0,\infty ) in the case 0

• Referencias bibliográficas
  • Bennett, C., Sharpley, R.: Interpolation of Operators, Pure and Applied Mathematics, vol. 129. Academic Press, Boston (1988)
  • Gogatishvili, A., Křepela, M., Pick, L., Soudský, F.: Embeddings of classical Lorentz spaces involving weighted integral means. (2016)
  • Gogatishvili, A., Kufner, A., Persson, L.-E.: Some new scales of weight characterizations of the class . Acta Math. Hung. 123, 365–377 (2009)
  • Gogatishvili, A., Mustafayev R.: Weighted iterated Hardy-type inequalities. (2015)
  • Gogatishvili, A., Opic, B., Pick, L.: Weighted inequalities for Hardy-type operators involving suprema. Collect. Math. 57, 227–255 (2006)
  • Gogatishvili, A., Persson, L.-E., Stepanov, V.D., Wall, P.: On scales of equivalent conditions that characterize the weighted Stieltjes inequality....
  • Gogatishvili, A., Persson, L.-E., Stepanov, V.D., Wall, P.: Some scales of equivalent conditions to characterize the Stieltjes inequality:...
  • Gogatishvili, A., Pick, L.: Duality principles and reduction theorems. Math. Inequal. Appl. 43, 539–558 (2000)
  • Gogatishvili, A., Pick, L.: A reduction theorem for supremum operators. J. Comput. Appl. Math. 208, 270–279 (2007)
  • Gogatishviliand, A., Stepanov, V.D.: Reduction theorems for operators on the cones of monotone functions. J. Math. Anal. Appl. 405, 156–172...
  • Goldman, M.L., Heinig, H.P., Stepanov, V.D.: On the principle of duality in Lorentz spaces. Can. J. Math. 48, 959–979 (1996)
  • Grosse-Erdmann K.-G.: The Blocking Technique, Weighted Mean Operators and Hardy’s Inequality, Lecture Notes in Mathematics, 1679. Springer-Verlag,...
  • Sinnamon, G.: Transferring monotonicity in weighted norm inequalities. Collect. Math. 54, 181–216 (2003)